| Abstract: |
| We discuss the existence of large-data global-in-time weak solutions to an evolutionary PDE system describing flows of incompressible heat-conducting viscoelastic fluids with stress-diffusion, subject to a stick-slip boundary condition for the velocity and a homogeneous Neumann boundary condition for the elastic part of the Cauchy stress tensor, which is supposed to be purely spherical. While the modelling assumption that the elastic part of the Cauchy stress tensor is purely spherical may render the system of governing equations under consideration restrictive from the physical point of view, the model nevertheless exhibits features that require novel mathematical ideas in order to deal with the technically complex structure of the associated internal energy and the more complicated forms of the corresponding entropy and energy fluxes. The concept of solution is motivated by the thermodynamical foundations of the model. |
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